We can observe propagation of excitation waves in some types of spatially distributed excitable media. Well known and important examples of such media are the nerve axon as an electrophysiological pulse transmission line and the Josephson junction strip as a cryo-electronic pulse transmission line. The aim of this project is to make clear, through mathematical analysis and numerical computations, general qualitative features of various types of excitation waves observed in the these media, e.g., solitary waves, periodic wavetrains, center waves, trains of mixed waves, standing waves and chaotic waves. We studied general geometrical properties of the solitary waves and the periodic wavetrains, and introduced some topological characteristics of these waves. By the use of these characteristics, we succeeded in understanding mechanisms of various bifurcations of the waves (i.e. the transitions from one type of wave to another) and in obtaining conditions for the stability and the instability of the waves. We introduced a kinematic consideration with respect to mutual interactions of impulse waves, based upon the dispersion relation of periodic wavetrains. By the use of this approximate consideration, we could understand some odd behavior of pulse trains such as the instability of equally spaced wavetrains, the formation of unequally spaced periodic wavetrains and the formation of bunches of densely aggregated pulses.